Abstract not found

Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type and module system, Standard ML manages to combine safety, security, and robustness with much of the flexibility of dynamically typed languages like Lisp. It is also has the most well-developed scientific foundation of any major language. Here I review the strengths and weaknesses of Standard ML and describe some of what we have learned through the design, implementation, and use of the language.

In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theorem prover (we call these tactics, Program Tactics). MT is expressive enough to represent the most interesting tacticals, i.e. then, orelse, try, progress and repeat. repeat allows us to express Logic Tactics which correspond to Program Tactics which may not terminate. This work is part of a larger project which aims at the development and mechanization of a metatheory which can be used to reason about, extend and, possibly, modify the code implementing Program Tactics and the GETFOL basic inference rules.

We consider evaluation strategies for database queries expressed in three functional query languages: the complex value algebra, the simply typed lambda calculus, and method schemas. Each of these query languages derives its expressive power from a different primitive: the complex value algebra from the powerset operator, the simply typed lambda calculus from list iteration, and method schemas from recursion. We show that "natural" evaluation strategies for these primitives may lead to very inefficient space usage, but that with some simple optimizations many queries can be evaluated with little or no space overhead. In particular, we show: (1) In the complex value algebra, all expressions with set nesting depth at most 2 can be evaluated in pspace, and this set of expressions is sufficient to express all queries in the polynomial hierarchy; (2) In the simply typed lambda calculus with equality and constants, all query terms of order at most 5 (where "query term" is a syntactic condition on types) can be evaluated in pspace, and this set of terms expresses exactly the pspace queries; (3) There exists a set of second-order method schemas (with no simple syntactic characterization) that can be evaluated in pspace, and this set of schemas is sufficient to express all pspace queries.

Computer programs may be regarded as formal mathematical objects whose properties are subject to mathematical proof. Program verification is the use of formal, mathematical techniques to debug software and software specifications. 1. Code Verification How are the properties of computer programs proved? We discuss three approaches in this article: inductive invariants, functional semantics, and explicit semantics. Because the first approach has received by far the most attention, it has produced the most impressive results to date. However, the field is now moving away from the inductive invariant approach. 1.1. Inductive Assertions The so-called Floyd-Hoare inductive assertion method of program verification [25, 33] has its roots in the classic Goldstine and von Neumann reports [53] and handles the usual kind of programming language, of which FORTRAN is perhaps the best example. In this style of verification, the specifier "annotates " certain points in the program with mathematical assertions that are supposed to describe relations that hold between the program variables and the initial input values each time "control " reaches the annotated point. Among these assertions are some that characterize acceptable input and the desired output. By exploring all possible paths from one assertion to the next and analyzing the effects of intervening program statements it is possible to reduce the correctness of the program to the problem of proving certain derived formulas called verification conditions. Below we illustrate the idea with a simple program for computing the factorial of its integer input N flowchart assertion start with input(N) input N A: = 1 N = 0 yes stop with? answer A

We present a safe embedding of mutable data structures in functional languages. With safety we mean that confluence and (in some sense) referential transparency are maintained. We develop a static criterion based on abstract interpretation which checks that any side-effect which a function may exert via a destructive update remains invisible. The technique opens up the possibility of designing safe and efficient wide-spectrum languages which combine functional and imperative language constructs.

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We address the “multicore problem ” for mathematical assistants with full proof checking, with special focus on Isabelle/Isar and its main SML platform Poly/ML. On the one hand, working with explicit definitions, statements, and proofs requires significant runtime resources, so the question of parallel checking is really relevant. On the other hand, the inherent structure of formal theories provides various possibilities for parallelism (both implicit and explicit), which is in fact an almost ideal situation. Exploiting this potential in practice requires to reconsider various aspects of the ML platform, the inference engine, and some higher prover specific layers. We report on an implementation of all that for Isabelle/Isar, and point out some general considerations for parallelism in functional programming, and other provers like Coq and HOL. Categories and Subject Descriptors D.1.3 [Concurrent Programming]: Parallel programming; I.2.3 [Deduction and Theorem

Abstract. PVS (Prototype Verification System) is a comprehensive framework for writing formal logical specifications and constructing proofs. An interactive proof checker is a key component of PVS. The capabilities of this proof checker can be extended by defining proof strategies that are similar to LCF-style tactics. Commonly used proof strategies include those for discharging typechecking proof obligations, simplification and rewriting using decision procedures, and various forms of induction. We describe the basic building blocks of PVS proof strategies and provide a pragmatic guide for writing sophisticated strategies. 1

The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides basic concepts to be incorporated into an innovative theorem prover to support interactive proofs construction in general domains. 1